# Laser focusing, minimum beam width

1. Aug 5, 2011

### Jimbone

I need to know the beam width of a pulsed yag laser (280.5 nm) when focused, assuming its completely guassian. The laser is focused through a bi-convex lens with f=15cm. I've found expressions for w(z), but they are all in terms of the minimum waist, w0, which I dont have and is probably the number I need. Can I some how approximate the beam width before or some distance after the lens, as it is on the order of mm on a business card, and use this to find my minimum waist after focused as well as w(z)?

Another problem I see is that I doubt the gaussian width I see on a business card reflects accurately the size, I've read what you see is about two times the actual width (as it is mostly fluorescance) ?

thanks

2. Aug 5, 2011

### Cthugha

The minimal achievable beam width also depends on the diameter of the collimated beam. The larger that diameter is, the smaller is the spot you can get. I suppose your equations give the minimum beam diameter as a function of the diameter at some other position or can be at least brought into such a form. For not too large f-numbers you can also approximate:
$$2 w_0=\frac{4 \lambda f}{\pi d}$$ where f is the focal length of the lens and d is the diameter of the collimated beam. See for example the following tutorial: http://www.newport.com/servicesupport/Tutorials/default.aspx?id=112" [Broken].

For not too faulty optics and not too long focal lengths the optimal beam width you see at a business card is in the micrometer range anyway and I doubt that you can judge the diameter with your naked eye. I am not able to tell the spot sizes of the laser beam in my lab accurately without using beam profilers or something like that.

Last edited by a moderator: May 5, 2017
3. Aug 5, 2011

### Jimbone

Thanks that looks good.

The laser image visible on a business card before the laser is focused is about 2 mm in diameter, it may be that it spreads out when it hits the business card? Either way I certainly can make a measurement of its visual size when it's nominally collimated.

4. Aug 5, 2011

### Andy Resnick

Another approach is to use the fact that (beam waist * divergence angle) is a constant for a Gaussian beam- if you know the beam parameters for the initial beam, you can easily calculate what happens after passing through a lens.

That said, you mention the beam is pulsed, with a (center?) wavelength of 280 nm- if you are using a lens designed for visible light (say BK-7 or something like that), the lens parameters may not be correct. Also, if the wavelength spread is large (fs-pulses?), chromatic aberration will have major effects.

As for using fluorescence to visually determine the beam waist, I agree with Cthugha. Why not image the beam waist onto a CCD? I've also seen people use a photocuring polymer to get UV beam profiles.

5. Aug 5, 2011

### Jimbone

Yes the laser is centered at 280.5 nm. The lens is UV quartz and the pulses are ns, should I still need to consider aberration? I think I am going to try to image the waist with a CCD so I can be sure I know what's going on. Never attempted that before, from the side wouldn't you see some N2 fluorescence?

So the laser fluorescence I'm seeing on the business card is not accurate (I am seeing a spot size of a few mm) ? Is the beam dispersing or spreading out on the card?

6. Aug 5, 2011

### Cthugha

That depends on how broad your light is in the spectral domain. This is of course a problem for femtosecond pulses as they are necessarily very broad. If your pulse is transform limited or at least close to it, there should not be significant problems for nanosecond pulses.

Just be careful not to saturate your CCD. If you do that you get blooming and your spot appears larger than it actually is. If your spot on the CCD gets smaller if you insert a neutral density attenuating filter, the spot size seen without the filter is larger than the real spot size.

This is quite possible, but I assume it should be possible to distinguish your laser and that fluorescence spectrally. Nitrogen fluorescence is strongest in the region from 310 to 380 nm, if I remember correctly. However, I might be wrong about that.

7. Aug 5, 2011

### Jimbone

I'm hesitant to send the laser directly at the CCD, even with a filter. Although it seems the most direct route. I'm running about 5 mJ/10 ns so that's a decent amount of power. I just need to get a rough idea of my spot size, I'm attempting to accurately hit the center of a 100 micro m diameter plasma so I'd like my waist to be a small fraction of that.

If I were to see some fluorescence from the profile of the waist I though I suppose I would only be seeing the portion of the laser that was able to excite the N2.

My FWHM is maybe 1 nm, so I'm guessing any lens aberration shouldn't be an issue.

8. Aug 5, 2011

### Andy Resnick

It's probably not a problem- ns pulses have (relative) spectral widths of 10^9 Hz, which is a few GHz in the UV. You are basically monochromatic. Using quartz was a smart decision also.

Not sure about N2 fluorescence. What's the pulse energy? I'm thinking about CCD damage, so if you are not sure, just put a ND filter in front of the CCD.

Depends on what you mean by 'accurate'- within 30%? 3%? 0.3%? There's nothing wrong with your method as a rough estimate.

9. Aug 15, 2011

### Jimbone

Ok, so I had previously determined from the theoretical expression for focused gaussian beam width and the business card image that the laser focused to a width of around 10-20 microns. I set up our CCD so that I could observe N2 fluorescence around 300 nm and measured a width of around 150 microns. Assuming the fluorescence was in focus, can I assume the laser is relatively the same size? Will the fluorescence be less localized than the laser itself?

I tend to trust the second measurement more than the first, although it makes my experiment all the more difficult.

And I've asked my colleagues and unfortunately it seems they'd rather not have me image the laser waist directly with CCD, even with a neutral filter.

10. Aug 15, 2011

### Jimbone

There was much more intense fluorescence in the 390 nm range, which gave a beam width of ~80 microns.